From 1940 he was a professor at Yale University, where he published his biography of Domenico Scarlatti and a critical edition of 60 sonatas by Scarlatti (1953). Scarlatti's sonatas are now conventionally designated by their Kirkpatrick numbers (shown as Kk. --, and more recently with a single K.), which is now considered the standard, authoritative numbering system for these works (despite at least two rival systems)[1] (see opus number).

During the 1960s Kirkpatrick made recordings of the complete harpsichord works of Johann Sebastian Bach (Archiv). The instrument he used in these recordings was always one or other of the contemporary harpsichords being made at the time by the firm of JC Neupert of Bamberg. These days such instruments are called "revival" style instruments, their features including 'inauthentic' metal frames and robust, heavy construction. These recordings show Kirkpatrick's formidable keyboard technique to full advantage, and, unusually for recordings of the time, he observes almost all of the repeats. His performances of The Well-Tempered Clavier were recorded on both the harpsichord and the clavichord. His later Bach recordings used a reproduction French harpsichord by Hubbard & Dowd.

He produced an edition of Bach's Goldberg Variations (1938, G. Schirmer, Inc. New York - 37149) which includes extensive discussion of ornamentation, fingering, phrasing, tempo, dynamics, and general interpretation. He also authored the posthumously published Interpreting Bach's Well-Tempered Clavier: A Performer's Discourse.

Kirkpatrick also played modern music, including Quincy Porter's Concerto for Harpsichord and Orchestra, Darius Milhaud's Sonata for Violin and Harpsichord, and the Double Concerto for Harpsichord, Piano and Chamber Orchestra by Elliott Carter, which was dedicated to him.

As a performer and recording artist, he became best known for his harpsichord performances of the keyboard music of Bach and Scarlatti. He also recorded on the clavichord (e.g. Bach's two- and three-part inventions, as well as both volumes of The Well-Tempered Clavier) and on the fortepiano (especially works by Mozart). He recalled playing a clavichord at a house concert in Hamburg, Germany.[2]